M. Wilkens et al., Transition temperature of the weakly interacting Bose gas: perturbative solution of the crossover equations in the canonical ensemble, J PHYS B, 33(20), 2000, pp. L779-L786
Citations number
25
Categorie Soggetti
Physics
Journal title
JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS
We compute the shift of the critical temperature T-c with respect to the id
eal case for a weakly interacting uniform Bose gas. We work in the framewor
k of the canonical ensemble, extending the criterion of condensation provid
ed by the canonical particle counting statistics for the zero-momentum stat
e of the uniform ideal gas. The perturbative solution of the crossover equa
tion to lowest order in powers of the scattering length yields (T-c - T-c(0
))/T-c(0) = -0.93a rho (1/3), where T-c(0) is the transition temperature of
the corresponding ideal Bose gas, a is the scattering length, and rho is t
he particle number density. This result is at variance with the standard gr
and canonical prediction of a null shift of the critical temperature in the
lowest perturbative order. The non-equivalence of statistical ensembles fo
r the ideal Bose gas is thus confirmed (at the lowest perturbative level) a
lso in the presence of interactions.